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基于地球物理、地球化学和冶金学的研究,现已确定地核由铁和少量轻元素组成,如氧(O)、硫(S)、硅(Si)、碳(C)和氢(H)[1]。由于Si在地球中的含量非常高[1-2],高温高压下在铁中的溶解度也很高[3-7],并且铁与硅酸盐反应会生成硅铁合金[8-9],因此Si被认为是地核中的主要轻元素。
目前,有关Si元素在内地核中的含量(以下如无特别说明,均为质量分数)仍然存在争议。例如:Lin等[10]测量了300 K下Fe-Si体系的状态方程,认为内核中存在约4%的Si;Asanuma等[11]分别测量了hcp-Fe0.93Si0.07在374 GPa和hcp-Fe0.83Ni0.09Si0.08在252 GPa压力下的状态方程,并由此预测内地核中含有3.9%~5.8%的Si;基于实验数据和第一性原理计算结果,Fischer等[5]认为内地核中Si的含量为6%~8%;Tateno等[6]根据实验测量结果推测内核中含有约7%的Si。
地核中的候选轻元素除了满足密度约束条件外,还应满足声速的约束条件。2007年,Badro等[12]采用非弹性X射线散射技术(Inelastic X-ray Scattering,IXS)对FeSi在78 GPa下的声速进行研究,预测内地核中Si的含量为2.8%。Antonangeli等[13]使用相同的技术对Fe0.89Ni0.04Si0.07在108 GPa下的声速进行研究,认为内地核中Si的含量为1%~2%。2012年,Mao等[14]采用IXS和X射线衍射(X-Ray Diffraction,XRD)技术对hcp-Fe和hcp-Fe0.85Si0.15的声速进行研究,估测内地核中Si的含量为8%。Liu等[15]分别测量了206 GPa以内hcp-Fe和136 GPa以内hcp-Fe86.8Ni8.6Si4.6的声速,认为内地核中Si的含量为2.3%。最近,Sakairi等[16]通过高压实验研究了hcp-Fe0.89Si0.11(Fe-6%Si)的声速,指出内核中存在3%~6%的Si。Antonangeli等[17]测量了300 K下hcp-Fe和hcp-Fe-9%Si在高压下的声速,认为内核的Si不超过(3±2)%。受实验技术的限制,上述声速测量所能达到的温度和压强条件远小于内地核的温压环境,因此在外推过程中不可避免地引入了误差。
基于密度泛函的第一性原理计算方法将不受上述条件的约束。Tsuchiya等[18]应用第一性原理方法计算了Fe-3.24%Si在0 K时的弹性常数,发现fcc (面心立方)结构和hcp(六方密堆积)结构的密度-速度关系与内地核数据一致。同样,运用第一性原理计算方法,Côté等[19]发现Fe-Si合金的结构与Si的含量有关:当Si的含量小于7%时,Fe-Si合金的结构为hcp结构;当Si的含量超过7%且温度高于4 000 K时,Fe-Si合金为fcc结构。Martorell等[20]计算了360 GPa时不同温度下的声速,认为Si不可能是内地核中的主要轻元素。综上所述,内地核中Si元素的含量还存在较大的争议,需要进一步开展理论和实验研究。
Fe-3.24%Si的状态方程和声速的第一性原理计算:地球内核Si元素的约束
First-Principles Calculations of the Equation of State and Sound Velocity of Fe-3.24%Si: Implications for the Composition of Earth’s Inner Core
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摘要: 硅(Si)被认为是地球内核的主要轻元素,但其在内地核中的含量仍然存在争议。为了探索内地核中Si的含量,应用第一性原理方法对Fe-3.24%Si(Si的质量分数为3.24%)进行了研究。构造了4种Fe-3.24%Si的超晶胞,研究了不同的晶胞大小和自旋对优化结构的影响。结果表明:在100 GPa以上,自旋对Fe-3.24%Si的密度无影响;而在100 GPa以下,考虑自旋时的计算结果更接近实验值。基于0 K下的声速、状态方程和相关热力学参数,计算了Fe-3.24%Si在内地核条件下的密度和声速。研究发现:Fe-3.24%Si的密度低于纯铁的密度,略高于内地核的密度;纵波声速及剪切波声速与纯铁的声速很接近,但均明显高于内地核声速,因此排除了内地核含有大量Si元素的可能性。
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关键词:
- Fe-3.24%Si /
- 第一性原理计算 /
- 状态方程 /
- 声速 /
- 内地核 /
Abstract: Silicon (Si) is considered as one major light element in Earth’s inner core, but its content is still controversy. In order to constrain its content in the inner core, using first-principles calculation method, we constructed four different supercells of Fe-3.24%Si and investigated the effects of cell size and spin on geometry optimization. It is found that the spin doesn’t affect the equation of state of Fe-3.24%Si above 100 GPa, and below 100 GPa, the calculated results with the spin are closer to the experimental data. Based on the equation of state, the sound velocity at 0 K and the corresponding thermodynamic parameters, the density and sound velocity of Fe-3.24%Si are obtained under the conditions of the inner core. The density of Fe-3.24%Si is lower than that of pure iron and slightly higher than that of the inner core. The sound velocities of longitudinal wave and shear wave for Fe-3.24%Si are very close to that of pure iron, but both are significantly higher than that of the inner core. Therefore, we could exclude the possibility that Earth’s inner core contains a large amount of Si.-
Key words:
- Fe-3.24%Si /
- first-principles calculation /
- equation of state /
- sound velocity /
- inner core /
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